Multiphase flows are relevant to various industrial processes and are also a ubiquitous feature of nature. Atomization is a Gas-Liquid class of multiphase flow in which the liquid bulk disintegrates into a spectrum of drops. The final drop size distribution of fragmenting liquids is important and is crucial to quantifying the performance of atomizers. This thesis implements two models of ligament breakup. The first model provides a method to determine the droplet size distribution of fragmenting ligaments. The second model provides a relation between ligament stretching, aspect ratio and dimensionless properties like Ohnesorge and Weber numbers for ligaments being stretched by aerodynamic force. The first model by Villermaux et.al considers a ligament as a linear succession of liquid blobs which undergo continuous interplay during destabilization. The evolution of their size distribution ultimately rules the droplet size distribution which follow a gamma distribution [14]. The results show that the Direct Numerical Simulations (DNS) of ligaments with different perturbations fragmented into very few drops and cannot be used to confirm that they follow the predicted gamma distribution. The second model considers a ligament breakup due to Rayleigh-Plateau Instability and provides an equation for ligament stretching. Through test runs the proportionality constant in the equation is determined by a least square fit. The theoretical number of drops is compared with the number of drops resulting from the Direct Numerical Simulation of ligament with a sinusoidal perturbation. It is found that the wavelength of the initial perturbation does not determine the number of drops obtained by ligament breakup

Realistic engineering, physical and biological systems are very complex in nature, and their response and performance are governed by multitude of interacting processes. In computational modeling of these systems, the interactive response is most often ignored, and simplifications are made to model one or a few relevant phenomena as opposed to a complete set of interacting processes due to a complexity of integrative analysis. In this thesis, I will develop new high-order computational approaches that reduce the amount of simplifications and model the full response of a complex system by accounting for the interaction between different physical processes as required for an accurate description of the global system behavior. Specifically, I will develop multi-physics coupling techniques based on spectral-element methods for the simulations of such systems. I focus on three specific applications: fluid-structure interaction, conjugate heat transfer, and modeling of acoustic wave propagation in non-uniform media. Fluid-structure interaction illustrates a complex system between a fluid and a solid, where a movable and deformable structure is surrounded by fluid flow, and its deformation caused by fluid affects the fluid flow interactively. To simulate this system, two coupling schemes are developed: 1) iterative implicit coupling, and 2) explicit coupling based on Robin-Neumann boundary conditions. A comprehensive verification strategy of the developed methodology is presented, including a comparison with benchmark flow solutions, h-, p- and temporal refinement studies. Simulation of a turbulent flow in a channel interacting with a compliant wall is attempted as well. Another problem I consider is when a solid is stationary, but a heat transfer occurs on the fluid-solid interface. To model this problem, a conjugate heat transfer framework is introduced. Validation of the framework, as well as studies of an interior thermal environment in a building regulated by an HVAC system with an on/off control model with precooling and multi-zone precooling strategies are presented. The final part of this thesis is devoted to modeling an interaction of acoustic waves with the fluid flow. The development of a spectral-element methodology for solution of Lighthill’s equation, and its application to a problem of leak detection in water pipes is presented.

Large amplitude westward propagating long waves in midlatitudes of Northern Hemisphere occasionally sustain coherent phase propagation over multiple weeks. Owing to the large amplitude and the life cycle of these waves previous studies have speculated their influence on extended-range weather forecasts but have not quantified them. The primary aim of this study is to establish an updated long-term catalog of Retrograde events which can then be used to investigate the statistics and structure of these waves. Guided by the newly created catalog the dynamics of these waves are further explored. A preliminary look into the dynamics of these waves reveal a sequence of poleward extrusion, westward migration and vortex shedding occurring frequently during certain strong Retrograde wave events. A strong connection between the westward moving low PV structures and the East Asian cold air outbreak is uncovered. Also, the initiation of the sequence of low PV extrusion and vortex shedding is found to be linked with the phase of propagating Wave-1 zonal component. Enhanced predictability of global midlatitude Geopotential Height at 500mb is noted during active period of strong Retrograde wave activity in comparison to inactive period. Skilled forecasts were produced almost (on an average) 12 days in advance during the active period of one of the winters (1995/96) as compared to 9 days during the inactive period of the season.

Drainage flow of a viscous compressible gas from a semi-sealed narrow conduit is a pore-scale model for studying the fundamental flow physics of fluid recovery from a porous reservoir without using fluid injection. Thermal effect has been routinely neglected for these flows in the traditional petroleum engineering literature. Since the motion is entirely driven by volumetric expansion, temperature change always accompanies the density change. This thesis examines such thermal effects on the drainage flow.

Thermal drainage flow is first studied by simultaneously solving the linearized continuity, momentum and energy equations for adiabatic walls. It is shown that even in the absence of an imposed temperature drop, gas expansion induces a transient temperature decrease inside the channel, which slows down the drainage process compared to the isothermal model and Lighthill’s model. For a given density drop, gas drains out faster as the initial-to-final temperature ratio increases; and the transient density can undershoot the final equilibrium value. A parametric study is then carried out to explore the influence of various thermal boundary conditions on drainage flow. It is found that as the wall transitions from adiabatic to isothermal condition, the excess density changes from a plane wave solution to a non-plane wave solution and the drainage rate increases. It is shown that when the exit is also cooled and the wall is non-adiabatic, the total recovered fluid mass exceeds the amount based on the isothermal theory which is determined by the initial and final density difference alone. Finally, a full numerical simulation is conducted to mimic the channel-reservoir system using the finite volume method. The Ghost-Cell Navier-Stokes Characteristic Boundary Condition technique is applied at the far end of the truncated reservoir, which is an open boundary. The results confirm the conclusions of the linear theory.

Compressible fluid flows involving multiple physical states of matter occur in both nature and technical applications such as underwater explosions and implosions, cavitation-induced bubble collapse in naval applications and Richtmyer-Meshkov type instabilities in inertial confinement fusion. Of particular interest is the atomization of fuels that enable shock-induced mixing of fuel and oxidizer in supersonic combustors. Due to low residence times and varying length scales, providing insight through physical experiments is both technically challenging and sometimes unfeasible. Numerical simulations can help provide detailed insight and aid in the engineering design of devices that can harness these physical phenomena.

In this research, computational methods were developed to accurately simulate phase interfaces in compressible fluid flows with a focus on targeting primary atomization. Novel numerical methods which treat the phase interface as a discontinuity, and as a smeared region were developed using low-dissipation, high-order schemes. The resulting methods account for the effects of compressibility, surface tension and viscosity. To aid with the varying length scales and high-resolution requirements found in atomization applications, an adaptive mesh refinement (AMR) framework is used to provide high-resolution only in regions of interest. The developed methods were verified with test cases involving strong shocks, high density ratios, surface tension effects and jumps in the equations of state, in one-, two- and three dimensions, obtaining good agreement with theoretical and experimental results. An application case of the primary atomization of a liquid jet injected into a Mach 2 supersonic crossflow of air is performed with the methods developed.

Phononic crystals are artificially engineered materials that can forbid phonon propagation in a specific frequency range that is referred to as a “phononic band gap.” Phononic crystals that have band gaps in the GHz to THz range can potentially enable sophisticated control over thermal transport with “phononic devices”. Calculations of the phononic band diagram are the standard method of determining if a given phononic crystal structure has a band gap. However, calculating the phononic band diagram is a computationally expensive and time-consuming process that can require sophisticated modeling and coding. In addition to this computational burden, the inverse process of designing a phononic crystal with a specific band gap center frequency and width is a challenging problem that requires extensive trial-and-error work.

In this dissertation, I first present colloidal nanocrystal superlattices as a new class of three-dimensional phononic crystals with periodicity in the sub-20 nm size regime using the plane wave expansion method. These calculations show that colloidal nanocrystal superlattices possess phononic band gaps with center frequencies in the 102 GHz range and widths in the 101 GHz range. Varying the colloidal nanocrystal size and composition provides additional opportunities to fine-tune the phononic band gap. This suggests that colloidal nanocrystal superlattices are a promising platform for the creation of high frequency phononic crystals.

For the next topic, I explore opportunities to use supervised machine learning for expedited discovery of phononic band gap presence, center frequency and width for over 14,000 two-dimensional phononic crystal structures. The best trained model predicts band gap formation, center frequencies and band gap widths, with 94% accuracy and coefficients of determination (R2) values of 0.66 and 0.83, respectively.

Lastly, I expand the above machine learning approach to use machine learning to design a phononic crystal for a given set of phononic band gap properties. The best model could predict elastic modulus of host and inclusion, density of host and inclusion, and diameter-to-lattice constant ratio for target center and width frequencies with coefficients of determinations of 0.94, 0.98, 0.94, 0.71, and 0.94 respectively. The high values coefficients of determination represents great opportunity for phononic crystal design.

This study explores the relationship between three physics-based predictive models defined by Castruccio et al. (2013), and four different distinct experimental morphologies of lava flows produced in a series of laboratory simulations where polyethylene glycol 600 (PEG) was pumped into an inclined chilled bath of water. The length of the experimental flow was recorded over time to create an experimental model to later be compared to the physics-based predictive models. The experimental morphologies are pillowed, rifted, folded, and leveed flows which can be characterized by a dimensionless parameter 𝛹, which scales natural lava flows to experimental lava flows and is a ratio of timescales, the characteristic timescale of thermal flux from the vent and the characteristic timescale of crust formation caused by surface cooling (Fink and Griffiths 1990). The three physics-based models are presented such that the downslope gravitational acceleration drives the flow, while either the Newtonian viscosity of the flow, the Yield Strength of the core (YS), or the Yield Strength of the growing crust (YSC) is the primary retarding factor in flow propagation. This study concluded that low 𝛹-value flows (low flux, low temperature, extensive crust formation) are better captured by the YSC model. And although the Newtonian model did not perfectly capture the behavior of any experimental flows in this study, high 𝛹-value flows (high flux, high temperature, little crust formation) that formed levees exhibited the most Newtonian behavior.

It is well known that radiative heat transfer rate can exceed that between two blackbodies by several orders of magnitude due to the coupling of evanescent waves. One promising application of near-field thermal radiation is thermophotovoltaic (TPV) devices, which convert thermal energy to electricity. Recently, different types of metamaterials with excitations of surface plasmon polaritons (SPPs)/surface phonon polaritons (SPhPs), magnetic polaritons (MP), and hyperbolic modes (HM), have been studied to further improve near-field radiative heat flux and conversion efficiency. On the other hand, near-field experimental demonstration between planar surfaces has been limited due to the extreme challenge in the vacuum gap control as well as the parallelism.

The main objective of this work is to experimentally study the near-field radiative transfer and the excitation of resonance modes by designing nanostructured thin films separated by nanometer vacuum gaps. In particular, the near-field radiative heat transfer between two parallel plates of intrinsic silicon wafers coated with a thin film of aluminum nanostructure is investigated. In addition, theoretical studies about the effects of different physical mechanisms such as SPhP/SPP, MPs, and HM on near-field radiative transfer in various nanostructured metamaterials are conducted particularly for near-field TPV applications. Numerical simulations are performed by using multilayer transfer matrix method, rigorous coupled wave analysis, and finite difference time domain techniques incorporated with fluctuational electrodynamics. The understanding gained here will undoubtedly benefit the spectral control of near-field thermal radiation for energy-harvesting applications like thermophotovoltaic energy conversion and radiation-based thermal management.

The world has been continuously urbanized and is currently accommodating more than half of the human population. Despite that cities cover only less than 3% of the Earth’s land surface area, they emerged as hotspots of anthropogenic activities. The drastic land use changes, complex three-dimensional urban terrain, and anthropogenic heat emissions alter the transport of mass, heat, and momentum, especially within the urban canopy layer. As a result, cities are confronting numerous environmental challenges such as exacerbated heat stress, frequent air pollution episodes, degraded water quality, increased energy consumption and water use, etc. Green infrastructure, in particular, the use of trees, has been proved as an effective means to improve urban environmental quality in existing research. However, quantitative evaluations of the efficacy of urban trees in regulating air quality and thermal environment are impeded by the limited temporal and spatial scales in field measurements and the deficiency in numerical models.

This dissertation aims to advance the simulation of realistic functions of urban trees in both microscale and mesoscale numerical models, and to systematically evaluate the cooling capacity of urban trees under thermal extremes. A coupled large-eddy simulation–Lagrangian stochastic modeling framework is developed for the complex urban environment and is used to evaluate the impact of urban trees on traffic-emitted pollutants. Results show that the model is robust for capturing the dispersion of urban air pollutants and how strategically implemented urban trees can reduce vehicle-emitted pollution. To evaluate the impact of urban trees on the thermal environment, the radiative shading effect of trees are incorporated into the integrated Weather Research and Forecasting model. The mesoscale model is used to simulate shade trees over the contiguous United States, suggesting how the efficacy of urban trees depends on geographical and climatic conditions. The cooling capacity of urban trees and its response to thermal extremes are then quantified for major metropolitans in the United States based on remotely sensed data. It is found the nonlinear temperature dependence of the cooling capacity remarkably resembles the thermodynamic liquid-water–vapor equilibrium. The findings in this dissertation are informative to evaluating and implementing urban trees, and green infrastructure in large, as an important urban planning strategy to cope with emergent global environmental changes.

This dissertation studies two outstanding microscale fluid mechanics problems: 1) mechanisms of gas production from the nanopores of shale; 2) enhanced mass flow rate in steady compressible gas flow through a micro-conduit.

The dissertation starts with a study of a volumetric expansion driven drainage flow of a viscous compressible fluid from a small capillary and channel in the low Mach number limit. An analysis based on the linearized compressible Navier-Stokes equations with no-slip condition shows that fluid drainage is controlled by the slow decay of the acoustic wave inside the capillary and the no-slip flow exhibits a slip-like mass flow rate. Numerical simulations are also carried out for drainage from a small capillary to a reservoir or a contraction of finite size. By allowing the density wave to escape the capillary, two wave leakage mechanisms are identified, which are dependent on the capillary length to radius ratio, reservoir size and acoustic Reynolds number. Empirical functions are generated for an effective diffusive coefficient which allows simple calculations of the drainage rate using a diffusion model without the presence of the reservoir or contraction.

In the second part of the dissertation, steady viscous compressible flow through a micro-conduit is studied using compressible Navier-Stokes equations with no-slip condition. The mathematical theory of Klainerman and Majda for low Mach number flow is employed to derive asymptotic equations in the limit of small Mach number. The overall flow, a combination of the Hagen-Poiseuille flow and a diffusive velocity shows a slip-like mass flow rate even through the overall velocity satisfies the no-slip condition. The result indicates that the classical formulation includes self-diffusion effect and it embeds the Extended Navier-Stokes equation theory (ENSE) without the need of introducing additional constitutive hypothesis or assuming slip on the boundary. Contrary to most ENSE publications, the predicted mass flow rate is still significantly below the measured data based on an extensive comparison with thirty-five experiments.